Deck 3: Describing Data: Numerical Measures

Question 1

The sum of the deviations of each data value from this measure of central location will always be zero.

A) Mode
B) Mean
C) Median
D) Standard deviation

Answer 1

B

Question 2

In a company, the standard deviation of the ages of female employees is six years and the standard deviation of the ages of male employees is ten years. These statistics indicate that the dispersion of age is greater for females than for males.

Answer 2

False

Question 3

The mean deviation is the difference between the mean or the deviations and the arithmetic mean.

Answer 3

False

Question 4

A set of ordinal, interval or ratio level data may only have one mode.

Question 5

The arithmetic mean is the sum of the quantitative observations divided by the total number of observations.

Question 6

According to Chebyshev's Theorem, 75% percent of the observations lie within plus and minus 2.00 average mean deviations.

Question 7

For any distribution, there are an equal number of values above and below the mean.

Question 8

For any data set, Chebyshev's Theorem estimates the proportion of observations that occurs within k standard deviations of the mean, where k is greater than 1.0.

Question 9

The variance is the mean of the sum of the squared deviations between each observation and the median.

Question 10

For any data set, which measures of central location have only one value?

A) Mode and median
B) Mode and mean
C) Mode and standard deviation
D) Mean and median

Question 11

The geometric mean is the nth root of n observations.

Question 12

Dispersion describes the degree of variation in the data.

Question 13

A value that is typical or representative of the data is referred to as a measure of central location.

Question 14

The standard deviation is the positive square root of the variance.

Question 15

Extremely high or low scores affect the value of the median.

Question 16

Three persons earn $8 an hour, six earn $9 an hour, and one earns $12 an hour. The weighted mean hourly wage is $9.

Question 17

The sum of the deviations from the mean for the set of numbers 4, 9 and 5 will equal zero.

Question 18

The mode is the value of the observation that appears most frequently.

Question 19

According to the Empirical Rule, 75% percent of the observations lie within plus and minus 2.00 average mean deviations.

Question 20

For a set of data arranged or sorted in numerical order, the value of the observation in the center is called the weighted mean.

Question 21

During the past six months, the purchasing agent bought: What is the weighted arithmetic mean price per ton?

A) $87.25
B) $72.33
C) $68.47
D) $89.18
E) $67.92

Question 22

The number of work stoppages in a highly industrialized region for selected months are: 6, 0, 10, 14, 8 and 0. What is the median number of stoppages?

A) 0
B) 6
C) 7
D) 8
E) 3

Question 23

A sample of single persons receiving social security payments revealed these monthly benefits: $826, $699, $1,087, $880, $839 and $965. How many observations are below the median?

A) 0
B) 1
C) 2
D) 3
E) 3.5

Question 24

What is the lowest level of measurement that a median can be computed?

A) Nominal
B) Ordinal
C) Interval
D) Ratio

Question 25

Fifteen accounting majors had an average grade of 90 on a finance exam. Seven marketing majors averaged 85, while ten finance majors averaged 93 on the same exam. What is the weighted mean for the 32 students taking the exam?

A) 89.84
B) 89.33
C) 89.48
D) Impossible to determine without more information

Question 26

A bottling company offers three kinds of delivery service - instant, same day and within five days. The profit per delivery varies according to the kind of delivery. The profit for an instant delivery is less than the other kinds because the driver has to go directly to a grocery store with a small load and return to the bottling plant. To find out what effect each type of delivery has on the profit picture, the company summarized the data in the following table based on deliveries for the previous quarter. What is the weighted mean profit per delivery?

A) $72
B) $110
C) $142
D) $97
E) $66.67

Question 27

A question in a market survey asks for a respondent's favorite car color. Which measure of central location should be used to summarize this question?

A) Mode
B) Median
C) Mean
D) Standard deviation

Question 28

Which one of the following is referred to as the population mean?

A) µ
B) s
C) $\sigma$
D) $\chi$

Question 29

Which measures of central location are not affected by extremely small or extremely large values?

A) Mean and median
B) Mean and mode
C) Mode and median
D) Standard deviation and mean

Question 30

The net incomes (in $millions) of a sample of steel fabricators are: $86, $67, $86 and $85. What is the modal net income?

A) $67
B) $85
C) $85.5
D) $86

Question 31

For a data set with an odd number of observations that have been sorted from smallest to largest values, where is the median located?

A) n
B) n/2
C) (n + 1)/2
D) n + ½

Question 32

Assume a student received the following grades for the semester: History, B; Statistics, A; Spanish, C; and English,

A) 4.00
B) 1.96
C) 2.76
C) History and English are 5 credit hour courses, Statistics a 4 credit hour course and Spanish a 3 credit hour course. If 4 grade points are assigned for an A, 3 for a B and 2 for a C, what is the weighted mean for the semester grades?
D) 3.01

Question 33

A sample of the paramedical fees charged by clinics revealed these amounts: $55, $49, $50, $45, $52 and $55. What is the median charge?

A) $47.50
B) $51.00
C) $52.00
D) $55.00

Question 34

On a survey questionnaire, students were asked to indicate their class in college. If there were only four choices from which to choose, which measure(s) of central location would be appropriate to use for the data generated by that questionnaire item?

A) Mean and median
B) Mean and mode
C) Mode and median
D) Mode only

Question 35

A stockbroker placed the following order for a customer:
*50 shares of Kaiser Aluminum preferred at $104 a share
* 100 shares of GTE preferred at $25.25 a share
* 20 shares of Boston Edison preferred at $9.125 a share
What is the weighted arithmetic mean price per share?

A) $25.25
B) $79.75
C) $103.50
D) $46.51

Question 36

What is the relationship among the mean, median and mode in a symmetric distribution?

A) They are all equal
B) The mean is always the smallest value
C) The mean is always the largest value
D) The mode is the largest value

Question 37

The lengths of time (in minutes) several underwriters took to review applications for similar insurance coverage are: 50, 230, 52 and 57. What is the median length of time required to review an application?

A) 54.5
B) 141.0
C) 97.25
D) 109.0

Question 38

What is the median of 26, 30, 24, 32, 32, 31, 27 and 29?

A) 32
B) 29
C) 30
D) 29.5

Question 39

For the most recent seven years, the U.S. Department of Education reported the following number of bachelor's degrees awarded in computer science: 4,033; 5,652; 6,407; 7,201; 8,719; 11,154; 15,121. What is the annual arithmetic mean number of degrees awarded?

A) About 12,240
B) About 8,327
C) About 6,217
D) About 15,962

Question 40

For a data set, half of the observations are always greater than the

A) Median
B) Mode
C) Mean
D) Standard deviation

Question 41

If the variance of the "number of daily parking tickets issued" is 100, the variance is defined as

A) "number of daily parking tickets".
B) "number of daily parking tickets" squared.
C) the absolute value of the "number of daily parking tickets".
D) the square root of the "number of daily parking tickets".

Question 42

What is a unique characteristic of the mean deviation?

A) It is based on only two observations.
B) It is based on deviations from the mean.
C) It uses absolute values.
D) It is only applied to skewed distributions.

Question 43

Rank the measures of dispersion in terms of their relative computational difficulty from least to most.

A) Mode, median, mean
B) Range, mean deviation, variance
C) Variance, mean deviation, range
D) There is no difference

Question 44

A purchasing agent for a trucking company is shopping for replacement tires for their trucks from two suppliers. The suppliers' prices are the same. However, Supplier A's tires have an average life of 60,000 miles with a standard deviation of 10,000 miles. Supplier B's tires have an average life of 60,000 miles with a standard deviation of 2,000 miles. Which of the following statements is true?

A) The two distributions of tire life are the same
B) On average, Supplier A's tires have a longer life then Supplier B's tires
C) The life of Supplier B's tire is more predictable than the life of Supplier A's tires
D) The dispersion of Supplier A's tire life is less than the dispersion of Supplier B's tire life

Question 45

Which of the following measures of dispersion are based on deviations from the mean?

A) Variance
B) Standard deviation
C) Mean deviation
D) All of the above

Question 46

Which measure of dispersion disregards the algebraic signs (plus and minus) of each difference between X and the mean?

A) Standard deviation
B) Mean deviation
C) Arithmetic mean
D) Variance

Question 47

According to Chebyshev's Theorem, at least what percent of the observations lie within plus and minus 1.75 standard deviations of the mean?

A) 56%
B) 95%
C) 67%
D) Cannot compute because it depends on the shape of the distribution

Question 48

For a sample of similar sized all-electric homes, the March electric bills were (to the nearest dollar): $212, $191, $176, $129, $106, $92, $108, $109, $103, $121, $175 and $194. What is the range?

A) $100
B) $130
C) $120
D) $112

Question 49

The following are the weekly amounts of welfare payments made by the federal government to a sample of six families: $139, $136, $130, $136, $147 and $136. What is the range?

A) $0
B) $14
C) $52
D) $17

Question 50

A disadvantage of using an arithmetic mean to summarize a set of data is that the arithmetic mean

A) sometimes has two values.
B) can be used for interval and ratio data.
C) is always different from the median.
D) can be biased by one or two extremely small or large values.

Question 51

Ten experts rated a newly developed chocolate chip cookie on a scale of 1 to 50. Their ratings were: 34, 35, 41, 28, 26, 29, 32, 36, 38 and 40. What is the mean deviation?

A) 8.00
B) 4.12
C) 12.67
D) 0.75

Question 52

The closing prices of a common stock have been 61.5, 62, 61.25, 60.875 and 61.5 for the past week. What is the range?

A) $1.250
B) $1.750 $1.125
D) $1.875

Question 53

What is a disadvantage of the range as a measure of dispersion?

A) Based on only two observations
B) Can be distorted by a large mean
C) Not in the same units as the original data
D) Has no disadvantage

Question 54

Sometimes, data has two values that have the highest and equal frequencies. In this case, the distribution of the data can best be summarized as

A) symmetric
B) bimodal (having two modes)
C) positively skewed
D) negatively skewed

Question 55

The mean, as a measure of central location would be inappropriate for which one of the following?

A) Ages of adults at a senior citizen center
B) Incomes of lawyers
C) Number of pages in textbooks on statistics
D) Marital status of college students at a particular university

Question 56

The weights of a sample of crates ready for shipment to Moscow, Russia are (in kilograms): 103, 97, 101, 106 and 103. What is the mean deviation?

A) 0 kg
B) 6.9 kg
C) 102.0 kg
D) 2.4 kg
E) 9.0 kg

Question 57

The weights (in kilograms) of a group of crates being shipped to Panama are 95, 103, 110, 104, 105, 112 and 92. What is the mean deviation?

A) 5.43 kg
B) 6.25 kg
C) 0.53 kg
D) 52.50 kg

Question 58

Rank the measures of dispersion in terms of their relative ease of interpretation from least to most.

A) Mode, median, mean
B) Range, mean deviation, variance
C) Variance, mean deviation, range
D) There is no difference

Question 59

The sum of the differences between sample observations and the sample mean is

A) Zero
B) The mean deviation
C) The range
D) The standard deviation

Question 60

What is the relationship between the variance and the standard deviation?

A) Variance is the square root of the standard deviation
B) Variance is the square of the standard deviation
C) Variance is twice the standard deviation
D) No constant relationship between the variance and the standard deviation

Question 61

What measure of central location uses all of the observations in its calculation? _____________

Question 62

A sample of the personnel files of eight male employees revealed that, during a six-month period, they lost the following number of days due to illness: 2, 0, 6, 3, 10, 4, 1 and 2. What is the mean deviation (in days)?

A) 1
B) 0
C) 3 1/8
D) 2 3/8

Question 63

The distribution of a sample of the outside diameters of PVC gas pipes approximates a symmetrical, bell-shaped distribution. The arithmetic mean is 14.0 inches, and the standard deviation is 0.1 inches. About 68 percent of the outside diameters lie between what two amounts?

A) 13.5 and 14.5 inches
B) 13.0 and 15.0 inches
C) 13.9 and 14.1 inches
D) 13.8 and 14.2 inches

Question 64

Based on the Empirical Rule, what percent of the observations will lie between plus or minus two standard deviations from the mean?

A) 95%
B) 5%
C) 68%
D) 2.5%

Question 65

Production of passenger cars in Japan increased from 3.94 million in 1999 to 6.74 million in 2009. What is the geometric mean annual percent increase?

A) 4.0
B) 1.9
C) 5.5
D) 16.6
E) 47.3

Question 66

In a frequency distribution, what measure of central location is used for the class with the largest number of observations? ______________

Question 67

A sample of assistant professors on the business faculty at state supported institutions in Ohio revealed the mean income to be $72,000 for 9 months with a standard deviation of $3,000. Using Chebyshev's Theorem, what proportion of the faculty earns more than $66,000 but less than $78,000?

A) At least 50%
B) At least 25%
C) At least 75%
D) At least 100%

Question 68

A sample of the monthly amounts spent for food by families of four receiving food stamps approximates a symmetrical distribution. The sample mean is $150 and the standard deviation is $20. Using the Empirical Rule, about 95 percent of the monthly food expenditures are between what two amounts?

A) $100 and $200
B) $85 and $105
C) $205 and $220
D) $110 and $190

Question 69

A population consists of all the weights of all defensive tackles on Sociable University's football team. They are: Johnson, 204 pounds; Patrick, 215 pounds; Junior, 207 pounds; Kendron, 212 pounds; Nicko, 214 pounds; and Cochran, 208 pounds. What is the population standard deviation (in pounds)?

A) About 4
B) About 16
C) About 100
D) About 40

Question 70

The U.S. Federal Aviation Administration reported that passenger revenues on international flights increased from $528 million in 1986 to $5,100 million in 2009. What is the geometric mean annual percent increase in international passenger revenues?

A) 10.4
B) 27.9
C) 103.6
D) 9.96
E) 2814

Question 71

If the sample variance for a frequency distribution consisting of hourly wages was computed to be 10, what is the sample standard deviation?

A) $1.96
B) $4.67
C) $3.16
D) $10.00

Question 72

The number of students at a local university increased from 2,500 students to 5,000 students in 10 years. Based on a geometric mean, the university grew at an average percentage rate of

A) 2,500 students per year
B) 1.071 percent per year
C) 7.1 percent per year
D) 250 students per year

Question 73

The weights (in grams) of the contents of several small bottles are 4, 2, 5, 4, 5, 2 and 6. What is the sample variance?

A) 6.92
B) 4.80
C) 1.96
D) 2.33

Question 74

Each person who applies for an assembly job at Robert's Electronics is given a mechanical aptitude test. One part of the test involves assembling a plug-in unit based on numbered instructions. A sample of the length of time it took 42 persons to assemble the unit was organized into the following frequency distribution. What is the standard deviation (in minutes)?

A) 3.89
B) 6.01
C) 8.78
D) 17.00

Question 75

The net annual sales of a sample of small retail clothing stores were organized into the following relative frequency distribution. What is the mean net sales (in $millions)?

A) $7.09
B) $10.09
C) $8.59
D) Mean cannot be computed

Question 76

The ages of all the patients in the isolation ward of the hospital are 38, 26, 13, 41 and 22. What is the population variance?

A) 106.8
B) 91.4
C) 240.3
D) 42.4

Question 77

Samples of the wires coming off the production line were tested for tensile strength. The statistical results (in PSI) were: According to the Empirical Rule, the middle 95 percent of the wires tested between approximately what two values?

A) 450 and 550
B) 460 and 540
C) 420 and 580
D) 380 and 620

Question 78

Which measure of central location is used to determine an average annual percent increase?

A) Arithmetic mean
B) Weighted mean
C) Mode
D) Geometric mean

Question 79

In the calculation of the arithmetic mean for grouped data, which value is used to represent all the values in a particular class?

A) The upper limit of the class.
B) The lower limit of the class.
C) The frequency of the class.
D) The cumulative frequency preceding the class.
E) The class midpoint.

Question 80

The Investment Research Institute reported in its Mutual Fund Fact Book that the number of mutual funds increased from 5725 in 1999 to 7977 in 2009. What is the geometric mean annual percent increase in the number of funds?

A) 1.034
B) 3.37
C) 39.34
D) 71.77
E) 633.5